Stochastic configuration network based on improved whale optimization algorithm for nonstationary time series prediction

The stochastic configuration network (SCN), a type of randomized learning algorithm, can solve the infeasible problem in random vector functional link (RVFL) by establishing a supervisory mechanism. The advantages of fast learning, convergence and not easily falling into local optima make SCN popular. However, the prediction effect of SCN is affected by the parameter settings and the nonstationarity of input data. In this paper, a hybrid model based on variational mode decomposition (VMD), improved whale optimization algorithm (IWOA), and SCN is proposed. The SCN will predict relatively stable data after decomposition by VMD, and parameters of SCN are optimized by IWOA. The IWOA diversifies the initial population by employing logistic chaotic map based on bit reversal and improves the search ability by using Levy flight. The exploration and exploitation of IWOA are superior to those of other optimization algorithms in multiple benchmark functions and CEC2020. Moreover, the proposed model is applied to the prediction of the nonstationary wind speeds in four seasons. We evaluate the performance of the proposed model using four evaluation indicators. The results show that the R-2 of the proposed model under four seasons are more than 0.999, and the root mean square error, mean absolute error, and symmetric mean absolute percentage error are less than 0.3, 0.17, and 13%, respectively, which are almost 1/10, 1/10, and 1/4 those of SCN, respectively.